Ionizing Radiation Interaction with Matter

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The discussion centers on the confusion regarding the derivation of the paths for incoming and outgoing photons in the context of ionizing radiation interaction with matter. The paths are defined as x=L/2 for incoming photons and x=r for outgoing photons, which raises questions about the assumptions made in the calculations. It is suggested that Tin represents the transmission factor before scattering, while Tout represents it after scattering, leading to uncertainty about the average photon path in the cylinder. The assumption that incoming photons do not converge towards the center while outgoing photons do is also questioned. Overall, clarity is sought on the rationale behind these specific path choices in the solution.
Graham87
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Homework Statement
Problem c)
Relevant Equations
Beer Lambert Law
##\phi(x) = \phi(0) e^{-\mu x}##
##T=e^{-\mu x}##
Screenshot 2024-10-30 104110.png


Basically, I don't understand how they got x=L/2 and x=r paths of T_in and T_out. Below is elaboration.

I don't understand the choice of paths for incoming and outgoing photons in the solution for c).
The solution put incoming path to x=L―/2, while outgoing x=r.
As I interpret it, Tin is the transmission factor before scattering, while Tout is the transmission factor after scattering?
The average photon path traveled in the cylinder is L― and we should divide by 2 for the average path L―/2 before scattering?
Why put the outgoing photons as r? So we assume the photons scatter in the center? But then again we assumed the incoming path is L―/2, which is an average that does not considers all traveling to the center.

So the incoming photons are not assumed to have a mutual path towards the center, while all the outgoing photons should be assumed to travel from the center?

Basically, I don't understand how they got x=L/2 and x=r paths of T_in and T_out.


Screenshot 2024-10-30 104059.png
 
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